Simulation intelligence: Towards a new generation of scientific methods
The original" Seven Motifs" set forth a roadmap of essential methods for the field of scientific
computing, where a motif is an algorithmic method that captures a pattern of computation …
computing, where a motif is an algorithmic method that captures a pattern of computation …
[图书][B] Uncertainty quantification: theory, implementation, and applications
RC Smith - 2024 - SIAM
Uncertainty quantification serves a central role for simulation-based analysis of physical,
engineering, and biological applications using mechanistic models. From a broad …
engineering, and biological applications using mechanistic models. From a broad …
Bayesian probabilistic numerical methods
Over forty years ago average-case error was proposed in the applied mathematics literature
as an alternative criterion with which to assess numerical methods. In contrast to worst-case …
as an alternative criterion with which to assess numerical methods. In contrast to worst-case …
Physics-informed Gaussian process regression generalizes linear PDE solvers
Linear partial differential equations (PDEs) are an important, widely applied class of
mechanistic models, describing physical processes such as heat transfer, electromagnetism …
mechanistic models, describing physical processes such as heat transfer, electromagnetism …
Position paper: Bayesian deep learning in the age of large-scale ai
In the current landscape of deep learning research, there is a predominant emphasis on
achieving high predictive accuracy in supervised tasks involving large image and language …
achieving high predictive accuracy in supervised tasks involving large image and language …
Position: Bayesian Deep Learning is Needed in the Age of Large-Scale AI
In the current landscape of deep learning research, there is a predominant emphasis on
achieving high predictive accuracy in supervised tasks involving large image and language …
achieving high predictive accuracy in supervised tasks involving large image and language …
Posterior and computational uncertainty in gaussian processes
Gaussian processes scale prohibitively with the size of the dataset. In response, many
approximation methods have been developed, which inevitably introduce approximation …
approximation methods have been developed, which inevitably introduce approximation …
[图书][B] Probabilistic Numerics: Computation as Machine Learning
Probabilistic numerical computation formalises the connection between machine learning
and applied mathematics. Numerical algorithms approximate intractable quantities from …
and applied mathematics. Numerical algorithms approximate intractable quantities from …
Bayesian ODE solvers: the maximum a posteriori estimate
There is a growing interest in probabilistic numerical solutions to ordinary differential
equations. In this paper, the maximum a posteriori estimate is studied under the class of ν ν …
equations. In this paper, the maximum a posteriori estimate is studied under the class of ν ν …
Parallel-in-time probabilistic numerical ODE solvers
Probabilistic numerical solvers for ordinary differential equations (ODEs) treat the numerical
simulation of dynamical systems as problems of Bayesian state estimation. Aside from …
simulation of dynamical systems as problems of Bayesian state estimation. Aside from …